It is well known that a borehole drilled into one of the earth's sedimentary basins encounters a succession of rock layers, usually of progressively increasing age. However, there are often gaps in the succession, representing periods of geologic time in which there was no deposition of sediments or in which sediments previously deposited were eroded by wind or water. The rock succession may therefore be viewed in terms of sequences of layers separated by sequence boundaries; within any sequence the rock layers result from quasi-continuous deposition of sediments, while at the sequence boundaries there is an interruption of deposition and often the loss of previous sediments.
Although the deposition of sediments within a sequence may be continuous, the rocks so formed are not uniform. Thus changes of climate at the source of the sediments affect the type and volume of sediments available for deposition; they also affect the manner and rate of transport of the sediments to the site of deposition. Further, the processes of basin formation necessarily induce subsidence, thus increasing the local depth of the sea and making more room available for deposition; the subsidence may be temporarily reversed by local tectonic uplift. And the global sea level is subject to rises and falls, reflecting in part the rearrangement of the oceans during plate movement and in part the climatic variations in the volume of the ice-caps. Any or all of these changes can affect the nature and volume of the sediments, and so the constitution and thickness of the rock layers.
These changes (and so the rock layers also) have an element of randomness, but also an element of order. For example, a river, delivering its sediments to the sea, may change its course by reason of some entirely fortuitous happening, but the climate--with its effect on both sediment volume and relative sea level--is known to relate to several independent and periodic perturbations of the orbit and inclination of the earth.
The element of order in rock successions, in one of its manifestations, was discovered by the present inventors, and reported in Geophysical Prospecting, vol 19, no 3, 1971. Expressed loosely, the conclusion was that, over a surprisingly large range of scales, a hard rock layer is more likely to be followed by a softer layer than by a harder layer, and a soft rock layer more likely to be followed by a harder layer than by a softer layer. This conclusion was evidenced by the observation that if the rock succession is expressed as a series of successive inter-layer contrasts, having both magnitude and sign, the autocorrelation function of this series is characterized by negative values at small lags. It may also be evidenced by the observation that the power spectrum of the series rises in approximate proportion to the first power of wavenumber. The range of scales over which these properties have been found to be general has been explored by Walden and Hosken in Geophysical Prospecting, vol 33, no 3, 1985.
These findings may also be related to the teachings of Mandelbrot (The Fractal Geometry of Nature, 1983). In particular, many natural processes (of which the deposition of sediments in layers is one) are seen to yield the property of scale invariance. In a crude sense, it has been known for many years that some geological successions have this property, while others do not; to cover the first case, all students of geology are trained to include a rule or a person or a coin (to give the scale) in any photograph of a rock outcrop.
It may therefore be asserted that geological successions within a sequence have an identifiable statistical property characteristic of uninterrupted deposition, and that this property is diminished or lost in successions that include one or more sequence boundaries. The property may be derived from a suitably adapted autocorrelation function, or from the spectral distribution, of some suitable measure of rock properties through the succession.